the centre of mass of three particles of masses 1 kg ,2 kg and 3 kg lies at the point (3 m,3 m,3 m). where should a fourth particle of mass 4 kg be positioned so that the centre of mass of the four particle system lies at the point (1 m,1 m,1 m)?
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As the c.m. of three particles is at (2,2,2) ∴The total mass = 1+2+3 = 6kg Now consider the 4kg mass at the position (x,y,z) Now centre of mass of total system at (0,0,0) ∴ 624 0 10 × + x = ⇒ 12 = -4x ⇒ x = -3 Similarly 624 0 12 × + y = ⇒ y = -3 624 0 12 × + z = ⇒ z = -3 From the above we can conclude that x = -3, y = -3, z = -3
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